In recent years, model predictive control (MPC) has been a leading technology for advanced process control (APC). MPC is running successfully in chemical/petrochemical plant units, thermal power plants, cement production lines, air separation units, building energy savings, etc. MPC differs from other control techniques in its implementation. At each sampling period, MPC optimizes a performance cost satisfying the physical constraints, to obtain a sequence of control moves. However, only the most recent control move among this sequence is implemented. This paradigm is called receding horizon optimization and control. MPC represents a unification of applied mathematics (optimization, stability analysis, etc.) to the automatic control of industrial facilities.

MPC is facing new mathematical and engineering challenges. The receding horizon optimization coincides with the common feature of daily life activities. For instance, human walking, driving, chess-playing, and studying are all receding horizon decision processes. The existing results of MPC are mostly based on difference/differential and state-space equations. They fit to some man-made processes, however, they are not ready to cover more heuristic/natural/inartificial activities. The theoretical analysis of the industrial MPC seems to be at the beginning stage. It is hard to further research this theoretical analysis due to the lack of appropriate mathematical frameworks. The syntheses of MPC with required stability and convergence properties have been developed. However, exact algorithms are not accepted in industrial circles. In a variety of engineering problems, there are several agents (controllers) with a shared control objective, for which the cooperative MPC and distributed MPC need further investigation. Both the industrial MPC and synthesis approaches need to be extended to a wider type of model (e.g., non-linear MPC). Some solvers for MPC are not fast enough to match the real dynamics. Intelligent techniques in artificial intelligence (AI) are being applied in MPC for modelling, prediction, and computation. Meanwhile, their adaptability to real applications and theoretical analyses needs to be demonstrated in broader terms. The applications of MPC to intelligent robots, smart homes, integrated energy management, and autonomous driving are currently being investigated. However, real applications using algorithms and frameworks are still lacking.

The aim of this Special Issue is to bring together original research and review articles highlighting the advances in model prediction control. We hope that this Special Issue provides a forum for researchers to summarize the most recent developments and ideas in the field. Moreover, we also wish that this Special Issue emphasizes mathematical and engineering results obtained within recent years.

Potential topics include but are not limited to the following:

• Synthesis approach of model prediction control
• Intelligent algorithm of model prediction control
• Double-layered model prediction control
• Hierarchical model prediction control
• Economic model prediction control
• Dynamic real-time optimization (RTO)
• Output feedback model prediction control
• Learning-based model prediction control
• Applications of model prediction control
• Industrial formulation of model prediction control
• Model prediction control in energy
• Non-linear model prediction control
• Model predictive controls with shared objectives (e.g., cooperative MPC, distributed MPC)